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The ponding problem on elastic membranes: An analog equation solution

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dc.contributor.author Katsikadelis, JT en
dc.contributor.author Nerantzaki, MS en
dc.date.accessioned 2014-03-01T01:18:26Z
dc.date.available 2014-03-01T01:18:26Z
dc.date.issued 2002 en
dc.identifier.issn 0178-7675 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/15001
dc.subject Boundary Condition en
dc.subject Equilibrium State en
dc.subject Integral Representation en
dc.subject Nonlinear Equation en
dc.subject Nonlinear Response en
dc.subject.classification Mathematics, Interdisciplinary Applications en
dc.subject.classification Mechanics en
dc.subject.other Boundary conditions en
dc.subject.other Boundary element method en
dc.subject.other Kinematics en
dc.subject.other Membranes en
dc.subject.other Nonlinear equations en
dc.subject.other Poisson equation en
dc.subject.other Ponding en
dc.subject.other Prestressing en
dc.subject.other Elastic membranes en
dc.subject.other Elasticity en
dc.title The ponding problem on elastic membranes: An analog equation solution en
heal.type journalArticle en
heal.identifier.primary 10.1007/s00466-001-0275-x en
heal.identifier.secondary http://dx.doi.org/10.1007/s00466-001-0275-x en
heal.language English en
heal.publicationDate 2002 en
heal.abstract In this paper, the nonlinear response of elastic membranes with arbitrary shape under partial and full ponding loads has been analyzed. Large deflections are considered, which result from nonlinear kinematic relations. The problem is formulated in terms of the displacements components and the three coupled nonlinear governing equations are solved using the analog equation method (AEM). The membrane may be prestressed either by prescribed boundary displacements or tractions. Using the concept of the analog equation the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on the BEM and the displacement components as well as the stress resultants at any point of the membrane are evaluated from their integral representations. In addition to the geometrical nonlinearity, the ponding problem is itself nonlinear, because the ponding load depends on the deflection surface that it produces. Iterative schemes are developed which converge to the equilibrium state of the membrane under the ponding loads. Several membranes are analyzed which illustrate the method and demonstrate its efficiency and accuracy. The method has all the advantages of the pure BEM, since the discretization and integration is limited only to the boundary. en
heal.publisher SPRINGER-VERLAG en
heal.journalName Computational Mechanics en
dc.identifier.doi 10.1007/s00466-001-0275-x en
dc.identifier.isi ISI:000174961100003 en
dc.identifier.volume 28 en
dc.identifier.issue 2 en
dc.identifier.spage 122 en
dc.identifier.epage 128 en


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